The number of points, where the function $f: \mathbf{R} \rightarrow \mathbf{R}$,
$f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\left|x^{2}-5 x+4\right|$, is NOT differentiable, is :
Solution
<p>$f:R \to R$.</p>
<p>$f(x) = |x - 1|\cos |x - 2|\sin |x - 1| + (x - 3)|{x^2} - 5x + 4|$</p>
<p>$= |x - 1|\cos |x - 2|\sin |x - 1| + (x - 3)|x - 1||x - 4|$</p>
<p>$= |x - 1|[\cos |x - 2|\sin |x - 1| + (x - 3)|x - 4|]$</p>
<p>Sharp edges at $x = 1$ and $x = 4$</p>
<p>$\therefore$ Non-differentiable at $x = 1$ and $x = 4$</p>
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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